Lecture/Notes 3.1
Problems 1-4, p.53
Handout - Section Review 1.3: due tomorrow
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Our Text
1 comment:
Quick Note:
This blog is not able to do superscripts (exponents), so I have used the ^ sign to show "to the."
So, 10^4 is ten to the fourth
Chapter 3.1
The Importance of Measurement
Qualitative and Quantitative Measurements
Qualitative Measurements - give results in a descriptive, nonnumeric (no numbers) form.
Examples: color, feelings, words like tall, short, hot, cold
Qualitative = quality - descriptions of things
Qualitative and Quantitative Measurements
Quantitative Measurements - gives results in a definite form - usually as numbers and units.
Examples: height in meters, temperature in degrees, distance in kilometers
Quantitative = quantity - think numbers
Scientific Notation
In science, we often come across very large or very small numbers.
For example, there are 602,000,000,000,000,000,000,000 particles in a mole of a substance.
Using scientific notation, we can write numbers like this in a shorter, easier to interpret form.
Scientific Notation
Scientific Notation - a way of writing numbers as a product of two numbers; a coefficient and 10 raised to a power.
Example: take the number 36,000 - in SN (scientific notation) we would write this as 3.6 x 10^4.
Scientific Notation, cont.
3.6 x 10^4 = first notice the coefficient
The coefficient is always between 1.0 and 10.0
Are the following correct coefficients?
2, 3.6, 9.999, 10.001, .9909
Scientific Notation, cont.
Let’s look at the exponent portion.
Remember our starting number was 36,000
What is our correct coefficient?
36,000?
3,600?
360?
36?
3.6?
0.36?
Scientific Notation, cont.
What would we have to multiply 3.6 by to get 36,000?
The answer is 10000 - or - 10^4. Notice 4 0’s = 10^4.
10x10x10x10
100x10x10
1,000x10
1,0000
SN Short-cut
Take the number 34,000,000
First find the number between 1 and 10 (the coefficient)
The number is 3.4 - assuming the decimal point is at the end, how many places would we have to count over?
34,000,000
We have to count over 7 places, so our answer is 3.4 x 10^7.
Try these:
Write 5.6 x 10^8 in standard form
Write 540,000,000,000 in SN
Small Numbers in SN
How would we write the number 0.000005 in SN.
The process is the same except for one part.
Rather then counting the 0’s from the right, we count them from the left (don’t count the zero before the decimal)
Small Numbers in SN, cont.
0.000005
First, find the coefficient. In this case, it is 5.
Now we count the decimal places - in other words, how many places do we have to move the decimal to get our coefficient?
0.000005
We would have to move the decimal 6 times to the right.
So, our SN number would be 5 x 10^-6.
Notice that we use negative exponents when the number is smaller than one.
Try these…
Convert the following numbers to SN
0.0000543; 45,000,000,000; 0.000000006
Convert the following from SN to standard form.
5.67 x 10^9; 3.8 x 10^-4; 1.01 x 10^-2; 1 x 10^1
Calculations in SN
Multiplication
First, multiply the coefficients.
Second, add the exponents
Third, adjust the coefficient and exponent, if necessary
SN - Multiplication
Example: 4.3 x 10^3 x 1.4 x 10^5
4.3 x 1.4 = 6.02
3 + 5 = 8
So, our answer is 6.02 x 10^8
SN - Multiplication
Let’s try a harder one:
5.8 x 10^-6 x 6.9 x 10^9
First: 5.8 x 6.9 = 40.02
-6 + 9 = 3
So, 40.02 x 10^3, but the coefficient is too big now, so we have to move the decimal; place one more to the left.
4.002 x 10^4
SN - Division
This is pretty much the opposite of multiplication
For this, we divide the coefficients and subtract the exponents
SN - Division
6.4 x 10^5 / 1.6 x 10^8
6.4/1.6 = 4
5 - 8 = -3
So, 4 x 10^-3
SN - Division
Try this one: 1.86 x 10^-4 / 9.3 x 10^-5
1.86 / 9.3 = ?
-4 - -5 = ?
Do we need to readjust?
SN - Division
1.86 / 9.3 = .15
-4 - -5 = 1
So, .2 x 10^1
What do we do now?
SN - Division
.2 x 10^1
2 x 10^0
100 = 1
So, 2 x 1
Or 2
SN - Addition and Subtraction
Addition and subtraction are a little more difficult.
The first step is to make both numbers have the same exponent.
Then, just add or subtract the coefficients and adjust.
SN - Addition and Subtraction
Let’s look at 3.4 x 10^4 + 1.2 x 10^5
First, make both exponents the same. It is usually easier to make the larger exponent smaller
So, 1.2 x 10^5 = 12 x 10^4
3.4 + 12 = 15.4 (line up the decimal)
15.4 x 10^4 = 1.54 x 10^5
Practice
Page 53, 1-4
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